Acta Applicandae Mathematicae

, Volume 97, Issue 1–3, pp 151–162 | Cite as

On Probability and Moment Inequalities for Supermartingales and Martingales

Article
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Abstract

Burkholder’s type inequality is stated for the special class of martingales, namely the product of independent random variables. The constants in the latter are much less than in the general case which is considered in Nagaev (Acta Appl. Math. 79, 35–46, 2003; Teor. Veroyatn. i Primenen. 51(2), 391–400, 2006). On the other hand, the moment inequality is proved, which extends these by Wittle (Teor. Veroyatn. i Primenen. 5(3), 331–334, 1960) and Dharmadhikari and Jogdeo (Ann. Math. Stat. 40(4), 1506–1508, 1969) to martingales.

Keywords

Martingale Supermartingale Submartingale Jensen inequality Holder inequality 
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Copyright information

© Springer Science + Business Media B.V. 2007

Authors and Affiliations

  1. 1.Sobolev Institute of MathematicsNovosibirskRussia

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